Modified Tseng's extragradient methods for variational inequality on Hadamard manifolds. Issue 12 (10th September 2021)

• Record Type: Journal Article
• Authors: Chen, Junfeng; Liu, Sanyang; Chang, Xiaokai
• Is Part Of: Applicable analysis. Volume 100:Issue 12(2021)
• Page Start: 2627
• Page End: 2640
• Publication Date: 2021-09-10
• Subjects: Variational inequalities -- extragradient method -- Hadamard manifolds -- pseudomonotone vector field; 47J20 -- 51H25 -- 65C10 -- 65C15 -- 90C33; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1695783
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: This paper is devoted to two efficient algorithms for solving variational inequality on Hadamard manifolds. The algorithms are inspired by Tseng's extragradient methods with new step sizes, established without the knowledge of the Lipschitz constant of the mapping. Under a pseudomonotone assumption on the underlying vector field, we prove that the sequence generated by the methods converges to a solution of variational inequality, whenever it exists.